2. Foundations of Astronomy: Part 4 Math and Astronomy Significant Figures Orders of Magnitude Units and Unit Conversions Nature of Science What is Science Terminology Scales Metric System Everyday Scales Astronomy Scales Modeling the Solar System

3. Scientific Notation (A shorthand way of writing very large and small numbers, which occur often in astronomy). We use powers, or exponents, of 10: 100 = 10 2 (= 10 x 10) 1000 = 10 3 (= 10 x 10 x 10) 1,000,000 = 10 6 10 = 10 1 1 = 10 0 0.1 = 10 -1 0.0001 = 10 -4 0.007 = 7 x 10 -3 4000 x 0.002 = (4 x 10 3 ) x (2 x 10 -3 ) = 8 x 10 0 = 8 Add the exponents

4. Examples: The mass of an electron 9.11 x 10 -31 kg The mass of the Earth 5.97 x 10 24 kg How many times more massive is the Earth than an electron?

5. Order of magnitude 100 = 10 2 (= 10 x 10) Order of Magnitude 100 or 2 1000 = 10 3 (= 10 x 10 x 10)1,000 or 3 1,000,000 = 10 6 1,000,000 or 6 10 = 10 1 10 or 1 1 = 10 0 1or 0 0.1 = 10 -1 0.1 or -1 0.0001 = 10 -4 0.0001 or -4 0.007 = 7 x 10 -3 0.01 or -2 Order of magnitude => round to nearest power of 10 Exponent of 10 is order of magnitude

6. Units and Unit Conversions How many seconds in a year?

7. Clicker Question: How many stars are there in the observable universe? A: 10 12 B: 10 22 C: 10 32 D: 10 42 E: infinite

8. Nature of Science What were the 3 most interesting things you found in the Einstein’s Big Idea Video? What is Science? How is it different from other areas of human activity? How is science done? Hypothesis vs. Theory Discuss 3 examples of science from the video? Terminology ObservationsScientific Statement Generalizations Simplifying Hypothesis Theory vs. Law

9. Foundations of Astronomy The Metric System (used by scientists and foreigners) Mass 1 kilogram (kg) = 1000 grams (g) 28 g = 1 ounce If your mass is 220 lbs, it's also 100 kg. We tend to use mass and weight interchangeably, but weight depends on gravity.

10. Distance 1 meter (m) = 100 centimeters (cm) = 39.4 inches (slightly longer than a yard - your professor is 1.8 m in height) 1 cm = 0.39 inches Volume 1 cubic centimeter or 1 cm 3 = 0.06 cubic inches (about the size of a sugar cube)

11. Temperature The Celsius Scale: T( o C ) = 5/9 [ T( o F) - 32 o F ] so 32 o F = 0 o C 212 o F = 100 o C 68 o F = 20 o C The Kelvin Scale: T(K) = T( o C) + 273 o C "Absolute zero" 0 K = -273 o C

12. Angular Measure 90 o 20 o 360 o, or 360 degrees, in a circle. 1 o = 60' or arcminutes 1' = 60" or arcseconds 1" = 1000 mas or milli-arcseconds

13. Full circle contains 360° (degrees). Each degree contains 60′ (arc-minutes). Each arc-minute contains 60″ (arc- seconds). Angular size of an object depends on actual size and distance away. Angular Measure

14. THE QUEST FOR RESOLUTION Jupiter and Io as seen from Earth 1 arcmin 1 arcsec 0.05 arcsec 0.001 arcsec Simulated with Galileo photo Atmosphere gives 1" limit without corrections which are easiest in radio

15. Scales of your world Think about How big your car is? How your house/apartment is? How big Albuquerque is? How big the US is? How far away the farthest place you have travelled is? How massive a very big man-made object is?

16. In astronomy, we deal with: 1. Vast distances - Radius of Earth = 6,400 km = 6.4 x 10 6 m - Distance to Moon =384,000 km = 3.8 x 10 8 m - Distance to Sun = 1.5 x 10 11 m = 23,500 Earth radii = 1 Astronomical Unit (AU) - Distance to next nearest star (Proxima Centauri): 270,000 AU = 4.3 "light years" (light year: distance light travels in one year, 9.5 x 10 12 km. Speed of light c = 3 x 10 8 m/sec) - Size of Milky Way Galaxy: about 100,000 light years - Distance to Andromeda Galaxy = 2.5 million light years - Distance to nearest cluster of galaxies (Virgo Cluster): 5 x 10 7 light years

17. 2. Huge masses: - Mass of Earth = 6 x 10 24 kg = 6 x 10 27 g = 1 M Earth (or 6000 billion billion tons) - Mass of Sun = 2 x 10 30 kg = 2 x 10 33 g = 1 M Sun = 1 "Solar Mass" = 333,000 M Earth - Mass of Milky Way galaxy: more than 10 11 M Sun - Mass of a typical cluster of galaxies: about 10 15 M Sun

18. 3. Long ages and times: - Age of Earth and Solar System: 4.5 billion years = 4.5 x 10 9 years - Lifetime of stars: about 10 6 - 10 10 years -Age of universe: about 10 10 years 4. Very high and low temperatures: - An interstellar "molecular cloud": T  10 K - Center of Sun: T = 1.5 x 10 7 K

19. Lecture Tutorial in Introductory Astronomy Check out online Applet http://physics.weber.edu/schroeder/sky/skymotionapplet.html http://physics.weber.edu/schroeder/sky/skymotionapplet.html Motion – Pages 1-6

20. Pre-Tutorial Question You are looking toward the north and see the Big Dipper to the right of Polaris. Fifteen minutes later, the Big Dipper will appear to have moved in roughly what direction? a)east (to your right) a)west (to your left) c)up (away from the horizon) c)down (closer to the horizon)